

<!DOCTYPE html>
<html lang="zh-CN" data-default-color-scheme=auto>



<head>
  <meta charset="UTF-8">
  <link rel="apple-touch-icon" sizes="76x76" href="/img/Mine.jpg">
  <link rel="icon" href="/img/Mine.jpg">
  <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=5.0, shrink-to-fit=no">
  <meta http-equiv="x-ua-compatible" content="ie=edge">
  
  <meta name="theme-color" content="#2f4154">
  <meta name="author" content="Chiam">
  <meta name="keywords" content="算法，安全">
  
    <meta name="description" content="『算法-ACM 竞赛-图论-次小生成树』洛谷 P4180 次小生成树洛谷 P 4180 次小生成树题目描述小 C 最近学了很多最小生成树的算法，Prim 算法、Kurskal 算法、消圈算法等等。正当小 C 洋洋得意之时，小 P 又来泼小 C 冷水了。小 P 说，让小 C 求出一个无向图的次小生成树，而且这个次小生成树还得是严格次小的，也就是说：如果最小生成树选择的边集是 EM，严格次小生成树选择">
<meta property="og:type" content="article">
<meta property="og:title" content="『算法-ACM竞赛-图论-次小生成树』洛谷P4180次小生成树">
<meta property="og:url" content="http://example.com/2023/12/06/%E3%80%8E%E7%AE%97%E6%B3%95-ACM%E7%AB%9E%E8%B5%9B-%E5%9B%BE%E8%AE%BA-%E6%AC%A1%E5%B0%8F%E7%94%9F%E6%88%90%E6%A0%91%E3%80%8F%E6%B4%9B%E8%B0%B7P4180%E6%AC%A1%E5%B0%8F%E7%94%9F%E6%88%90%E6%A0%91/index.html">
<meta property="og:site_name" content="Chiam 的个人主页">
<meta property="og:description" content="『算法-ACM 竞赛-图论-次小生成树』洛谷 P4180 次小生成树洛谷 P 4180 次小生成树题目描述小 C 最近学了很多最小生成树的算法，Prim 算法、Kurskal 算法、消圈算法等等。正当小 C 洋洋得意之时，小 P 又来泼小 C 冷水了。小 P 说，让小 C 求出一个无向图的次小生成树，而且这个次小生成树还得是严格次小的，也就是说：如果最小生成树选择的边集是 EM，严格次小生成树选择">
<meta property="og:locale" content="zh_CN">
<meta property="article:published_time" content="2023-12-05T16:11:44.640Z">
<meta property="article:modified_time" content="2023-12-05T16:18:59.163Z">
<meta property="article:author" content="Chiam">
<meta property="article:tag" content="算法，安全">
<meta name="twitter:card" content="summary_large_image">
  
  
  
  <title>『算法-ACM竞赛-图论-次小生成树』洛谷P4180次小生成树 - Chiam 的个人主页</title>

  <link  rel="stylesheet" href="https://lib.baomitu.com/twitter-bootstrap/4.6.1/css/bootstrap.min.css" />



  <link  rel="stylesheet" href="https://lib.baomitu.com/github-markdown-css/4.0.0/github-markdown.min.css" />

  <link  rel="stylesheet" href="https://lib.baomitu.com/hint.css/2.7.0/hint.min.css" />

  <link  rel="stylesheet" href="https://lib.baomitu.com/fancybox/3.5.7/jquery.fancybox.min.css" />



<!-- 主题依赖的图标库，不要自行修改 -->
<!-- Do not modify the link that theme dependent icons -->

<link rel="stylesheet" href="//at.alicdn.com/t/font_1749284_hj8rtnfg7um.css">



<link rel="stylesheet" href="//at.alicdn.com/t/font_1736178_lbnruvf0jn.css">


<link  rel="stylesheet" href="/css/main.css" />


  <link id="highlight-css" rel="stylesheet" href="/css/highlight.css" />
  
    <link id="highlight-css-dark" rel="stylesheet" href="/css/highlight-dark.css" />
  



  
<link rel="stylesheet" href="/css/custom.css">



  <script id="fluid-configs">
    var Fluid = window.Fluid || {};
    Fluid.ctx = Object.assign({}, Fluid.ctx)
    var CONFIG = {"hostname":"example.com","root":"/","version":"1.9.5-a","typing":{"enable":true,"typeSpeed":70,"cursorChar":"_","loop":false,"scope":[]},"anchorjs":{"enable":true,"element":"h1,h2,h3,h4,h5,h6","placement":"left","visible":"hover","icon":"❡"},"progressbar":{"enable":true,"height_px":3,"color":"#29d","options":{"showSpinner":false,"trickleSpeed":100}},"code_language":{"enable":true,"default":"TEXT"},"copy_btn":true,"image_caption":{"enable":true},"image_zoom":{"enable":true,"img_url_replace":["",""]},"toc":{"enable":true,"placement":"right","headingSelector":"h1,h2,h3,h4,h5,h6","collapseDepth":2},"lazyload":{"enable":true,"loading_img":"/img/loading.gif","onlypost":false,"offset_factor":2},"web_analytics":{"enable":false,"follow_dnt":true,"baidu":null,"google":{"measurement_id":null},"tencent":{"sid":null,"cid":null},"woyaola":null,"cnzz":null,"leancloud":{"app_id":null,"app_key":null,"server_url":null,"path":"window.location.pathname","ignore_local":false}},"search_path":"/local-search.xml","include_content_in_search":true};

    if (CONFIG.web_analytics.follow_dnt) {
      var dntVal = navigator.doNotTrack || window.doNotTrack || navigator.msDoNotTrack;
      Fluid.ctx.dnt = dntVal && (dntVal.startsWith('1') || dntVal.startsWith('yes') || dntVal.startsWith('on'));
    }
  </script>
  <script  src="/js/utils.js" ></script>
  <script  src="/js/color-schema.js" ></script>
  


  
<meta name="generator" content="Hexo 6.3.0"></head>


<body>
  

  <header>
    

<div class="header-inner" style="height: 70vh;">
  <nav id="navbar" class="navbar fixed-top  navbar-expand-lg navbar-dark scrolling-navbar">
  <div class="container">
    <a class="navbar-brand" href="/">
      <strong>Chiam&#39;s Blogs</strong>
    </a>

    <button id="navbar-toggler-btn" class="navbar-toggler" type="button" data-toggle="collapse"
            data-target="#navbarSupportedContent"
            aria-controls="navbarSupportedContent" aria-expanded="false" aria-label="Toggle navigation">
      <div class="animated-icon"><span></span><span></span><span></span></div>
    </button>

    <!-- Collapsible content -->
    <div class="collapse navbar-collapse" id="navbarSupportedContent">
      <ul class="navbar-nav ml-auto text-center">
        
          
          
          
          
            <li class="nav-item">
              <a class="nav-link" href="/">
                
                <span>首页</span>
              </a>
            </li>
          
        
          
          
          
          
            <li class="nav-item">
              <a class="nav-link" href="/archives/">
                
                <span>归档</span>
              </a>
            </li>
          
        
          
          
          
          
            <li class="nav-item">
              <a class="nav-link" href="/categories/">
                
                <span>分类</span>
              </a>
            </li>
          
        
          
          
          
          
            <li class="nav-item">
              <a class="nav-link" href="/about/">
                
                <span>关于</span>
              </a>
            </li>
          
        
          
          
          
          
            <li class="nav-item">
              <a class="nav-link" href="/links/">
                
                <span>友链</span>
              </a>
            </li>
          
        
        
          <li class="nav-item" id="search-btn">
            <a class="nav-link" target="_self" href="javascript:;" data-toggle="modal" data-target="#modalSearch" aria-label="Search">
              <i class="iconfont icon-search"></i>
            </a>
          </li>
          
        
        
          <li class="nav-item" id="color-toggle-btn">
            <a class="nav-link" target="_self" href="javascript:;" aria-label="Color Toggle">
              <i class="iconfont icon-dark" id="color-toggle-icon"></i>
            </a>
          </li>
        
      </ul>
    </div>
  </div>
</nav>

  

<div id="banner" class="banner" parallax=true
     style="background: url('/img/default.png') no-repeat center center; background-size: cover;">
  <div class="full-bg-img">
    <div class="mask flex-center" style="background-color: rgba(0, 0, 0, 0.3)">
      <div class="banner-text text-center fade-in-up">
        <div class="h2">
          
            <span id="subtitle" data-typed-text="『算法-ACM竞赛-图论-次小生成树』洛谷P4180次小生成树"></span>
          
        </div>

        
          
  <div class="mt-3">
    
    
      <span class="post-meta">
        <i class="iconfont icon-date-fill" aria-hidden="true"></i>
        <time datetime="2023-12-06 00:11" pubdate>
          2023年12月6日 凌晨
        </time>
      </span>
    
  </div>

  <div class="mt-1">
    
      <span class="post-meta mr-2">
        <i class="iconfont icon-chart"></i>
        
          2.9k 字
        
      </span>
    

    
      <span class="post-meta mr-2">
        <i class="iconfont icon-clock-fill"></i>
        
        
        
          25 分钟
        
      </span>
    

    
    
  </div>


        
      </div>

      
    </div>
  </div>
</div>

</div>

  </header>

  <main>
    
      

<div class="container-fluid nopadding-x">
  <div class="row nomargin-x">
    <div class="side-col d-none d-lg-block col-lg-2">
      

    </div>

    <div class="col-lg-8 nopadding-x-md">
      <div class="container nopadding-x-md" id="board-ctn">
        <div id="board">
          <article class="post-content mx-auto">
            <h1 id="seo-header">『算法-ACM竞赛-图论-次小生成树』洛谷P4180次小生成树</h1>
            
            
              <div class="markdown-body">
                
                <h1 id="『算法-ACM-竞赛-图论-次小生成树』洛谷-P4180-次小生成树"><a href="#『算法-ACM-竞赛-图论-次小生成树』洛谷-P4180-次小生成树" class="headerlink" title="『算法-ACM 竞赛-图论-次小生成树』洛谷 P4180 次小生成树"></a>『算法-ACM 竞赛-图论-次小生成树』洛谷 P4180 次小生成树</h1><h1 id="洛谷-P-4180-次小生成树"><a href="#洛谷-P-4180-次小生成树" class="headerlink" title="洛谷 P 4180 次小生成树"></a>洛谷 P 4180 次小生成树</h1><h3 id="题目描述"><a href="#题目描述" class="headerlink" title="题目描述"></a>题目描述</h3><p>小 C 最近学了很多最小生成树的算法，Prim 算法、Kurskal 算法、消圈算法等等。正当小 C 洋洋得意之时，小 P 又来泼小 C 冷水了。小 P 说，让小 C 求出一个无向图的次小生成树，而且这个次小生成树还得是严格次小的，也就是说：如果最小生成树选择的边集是 EM，严格次小生成树选择的边集是 ES，那么需要满足：(value(e)表示边 e 的权值) \sum*{e \in E_M}value(e)&lt;\sum*{e \in E_S}value(e)∑e∈EM​​value(e)&lt;∑e∈ES​​value(e)</p>
<p>这下小 C 蒙了，他找到了你，希望你帮他解决这个问题。</p>
<h3 id="输入格式"><a href="#输入格式" class="headerlink" title="输入格式"></a>输入格式</h3><p>第一行包含两个整数 N 和 M，表示无向图的点数与边数。 接下来 M 行，每行 3 个数 x y z 表示，点 x 和点 y 之间有一条边，边的权值为 z。</p>
<h3 id="输出格式"><a href="#输出格式" class="headerlink" title="输出格式"></a>输出格式</h3><p>包含一行，仅一个数，表示严格次小生成树的边权和。(数据保证必定存在严格次小生成树)</p>
<h3 id="输入输出样例"><a href="#输入输出样例" class="headerlink" title="输入输出样例"></a>输入输出样例</h3><p><strong>输入 #1</strong>复制</p>
<pre><code class="hljs">5 6
1 2 1
1 3 2
2 4 3
3 5 4
3 4 3
4 5 6
</code></pre>
<p><strong>输出 #1</strong>复制</p>
<pre><code class="hljs">11
</code></pre>
<h3 id="说明-提示"><a href="#说明-提示" class="headerlink" title="说明&#x2F;提示"></a>说明&#x2F;提示</h3><p>数据中无向图无自环； 50% 的数据 N≤2 000 M≤3 000； 80% 的数据 N≤50 000 M≤100 000； 100% 的数据 N≤100 000 M≤300 000 ，边权值非负且不超过 10^9 。</p>
<p><a target="_blank" rel="noopener" href="https://blog.csdn.net/weixin_43627118/article/details/102527903">题解</a></p>
<pre><code class="hljs">#include&lt;iostream&gt;
#include&lt;algorithm&gt;
#include&lt;vector&gt;
#include&lt;cstdio&gt;
typedef long long ll;
using namespace std;
const int M=1e5+100;
ll n,m,res,ans=0x3f3f3f3f,mx;
int f[M],fa[25][M],dep[M];
ll d[2][25][M];
bool used[3*M],vis[M];
vector&lt;int&gt; a[M];
struct Edge
&#123;
    int from, to;
    ll val;
    bool operator &lt; (const Edge y)
    &#123;
        return val &lt; y.val;
    &#125;
&#125; e[3*M];
int F(int x)
&#123;
    if(f[x]==x)
        return x;
    return f[x]=F(f[x]);
&#125;
void kruskal()  //kruskal 算最大生成树（已保证任意两点之间最小限重最优）
&#123;
    sort(e,e+m);
    int lef=n-1;
    for(int i=1; i&lt;=n; ++i)
        f[i]=i;
    for(int i=0; i&lt;m &amp;&amp; lef; ++i)
    &#123;
        int x=F(e[i].from),y=F(e[i].to);
        if(x!=y)
        &#123;
            f[x]=y;
            res+=e[i].val;
            used[i]=1;
            --lef;
            mx=max(mx, e[i].val);
        &#125;
    &#125;
&#125;
void dfs(int x)     //深搜建树（可能不止一棵，因为数据未保证是连通图）
&#123;
    vis[x]=true;
    for(int i=1; i&lt;=23; ++i)
    &#123;
        fa[i][x]=fa[i-1][fa[i-1][x]];
        ll t1=d[0][i-1][x], t2=d[0][i-1][fa[i-1][x]];
        d[0][i][x]=max(t1, t2);
        d[1][i][x]=max(d[1][i-1][x], d[1][i-1][fa[i-1][x]]);
        if(t1!=t2)
            d[1][i][x]=max(d[1][i][x], min(t1, t2));
    &#125;
    for(int i=0; i&lt;a[x].size(); ++i)
    &#123;
        int t=e[a[x][i]].to+e[a[x][i]].from-x;
        if(vis[t])
            continue;    //vis为1表示是父节点
        dep[t]=dep[x]+1;
        fa[0][t]=x;
        d[0][0][t]=e[a[x][i]].val;
        dfs(t);
    &#125;
&#125;
int lca(int u,int v)
&#123;
    if(dep[u]&lt;dep[v])
        swap(u,v);
    if(dep[u]!=dep[v])      //将深度做相等
    &#123;
        for(int i=23,h=dep[u]-dep[v]; i&gt;=0; --i)
            if(h&amp;(1&lt;&lt;i))
                u=fa[i][u];
    &#125;
    if(u==v)
        return u;  //如果已经在一个节点上就直接返回
    for(int i=23; i&gt;=0; --i)
        if(fa[i][u]!=fa[i][v])
            u=fa[i][u], v=fa[i][v];
    return fa[0][u];
&#125;
ll get(int u,int v,int c)
&#123;
    int fht=lca(u,v);
    ll m1=0,m2=0;
    for(int i=23,h1=dep[u]-dep[fht],h2=dep[v]-dep[fht]; i&gt;=0; --i)
    &#123;
        if(h1&amp;(1&lt;&lt;i))
        &#123;
            if(d[0][i][u]&gt;m1)
                m2=m1,m1=d[0][i][u];
            else if(d[0][i][u]&gt;m2)
                m2=d[0][i][u];
            else
                m2=max(m2, d[1][i][u]);
        &#125;
        if(h2&amp;(1&lt;&lt;i))
        &#123;
            if(d[0][i][v]&gt;m1)
                m2=m1,m1=d[0][i][v];
            else if(d[0][i][v]&gt;m2)
                m2=d[0][i][v];
            else
                m2=max(m2, d[1][i][v]);
        &#125;
    &#125;
    if(m1==c)
        return c-m2;
    else
        return c-m1;
&#125;
int main()
&#123;
    scanf(&quot;%d%d&quot;,&amp;n,&amp;m);
    for(int i=0; i&lt;m; ++i)
    &#123;
        int u,v;
        ll w;
        scanf(&quot;%d%d%lld&quot;,&amp;u,&amp;v,&amp;w);
        e[i].from=u;
        e[i].to=v;
        e[i].val=w;
    &#125;
    kruskal();
    for(int i=0; i&lt;m; ++i)
        if(used[i])
        &#123;
            a[e[i].from].push_back(i);
            a[e[i].to].push_back(i);
        &#125;
    dep[1]=1;
    dfs(1);
    for(int i=0; i&lt;m; ++i)
        if(!used[i])
        &#123;
            if(e[i].val-mx&gt;ans)
                break;
            ll t=get(e[i].from, e[i].to, e[i].val);
            ans=min(ans, t);
        &#125;
    return printf(&quot;%lld\n&quot;,res+ans),0;
&#125;
</code></pre>

                
              </div>
            
            <hr/>
            <div>
              <div class="post-metas my-3">
  
    <div class="post-meta mr-3 d-flex align-items-center">
      <i class="iconfont icon-category"></i>
      

<span class="category-chains">
  
  
    
      <span class="category-chain">
        
  <a href="/categories/%E7%AE%97%E6%B3%95/" class="category-chain-item">算法</a>
  
  
    <span>></span>
    
  <a href="/categories/%E7%AE%97%E6%B3%95/ACM%E7%AB%9E%E8%B5%9B/" class="category-chain-item">ACM竞赛</a>
  
  
    <span>></span>
    
  <a href="/categories/%E7%AE%97%E6%B3%95/ACM%E7%AB%9E%E8%B5%9B/%E5%9B%BE%E8%AE%BA/" class="category-chain-item">图论</a>
  
  
    <span>></span>
    
  <a href="/categories/%E7%AE%97%E6%B3%95/ACM%E7%AB%9E%E8%B5%9B/%E5%9B%BE%E8%AE%BA/%E6%AC%A1%E5%B0%8F%E7%94%9F%E6%88%90%E6%A0%91/" class="category-chain-item">次小生成树</a>
  
  

  

  

  

      </span>
    
  
</span>

    </div>
  
  
</div>


              
  

  <div class="license-box my-3">
    <div class="license-title">
      <div>『算法-ACM竞赛-图论-次小生成树』洛谷P4180次小生成树</div>
      <div>http://example.com/2023/12/06/『算法-ACM竞赛-图论-次小生成树』洛谷P4180次小生成树/</div>
    </div>
    <div class="license-meta">
      
        <div class="license-meta-item">
          <div>作者</div>
          <div>Chiam</div>
        </div>
      
      
        <div class="license-meta-item license-meta-date">
          <div>发布于</div>
          <div>2023年12月6日</div>
        </div>
      
      
      
        <div class="license-meta-item">
          <div>许可协议</div>
          <div>
            
              
              
                <a class="print-no-link" target="_blank" href="https://creativecommons.org/licenses/by/4.0/">
                  <span class="hint--top hint--rounded" aria-label="BY - 署名">
                    <i class="iconfont icon-by"></i>
                  </span>
                </a>
              
            
          </div>
        </div>
      
    </div>
    <div class="license-icon iconfont"></div>
  </div>



              
                <div class="post-prevnext my-3">
                  <article class="post-prev col-6">
                    
                    
                      <a href="/2023/12/06/%E3%80%8E%E7%AE%97%E6%B3%95-ACM%E7%AB%9E%E8%B5%9B-%E5%9B%BE%E8%AE%BA-%E7%BD%91%E7%BB%9C%E6%B5%81-%E6%9C%80%E5%B0%8F%E5%89%B2%E3%80%8F%20HDU%202485%20Destroying%20the%20bus%20stations%EF%BC%88%E6%9C%80%E7%9F%AD%E8%B7%AF+%E9%99%90%E6%B5%81%E5%BB%BA%E5%9B%BE%EF%BC%89/" title="『算法-ACM竞赛-图论-网络流-最小割』 HDU 2485 Destroying the bus stations（最短路+限流建图）">
                        <i class="iconfont icon-arrowleft"></i>
                        <span class="hidden-mobile">『算法-ACM竞赛-图论-网络流-最小割』 HDU 2485 Destroying the bus stations（最短路+限流建图）</span>
                        <span class="visible-mobile">上一篇</span>
                      </a>
                    
                  </article>
                  <article class="post-next col-6">
                    
                    
                      <a href="/2023/12/06/%E3%80%8E%E7%AE%97%E6%B3%95-ACM%E7%AB%9E%E8%B5%9B-%E5%9B%BE%E8%AE%BA-%E6%9C%80%E7%9F%AD%E8%B7%AF%E3%80%8F%E6%9C%80%E7%9F%AD%E8%B7%AF%E7%AE%97%E6%B3%95%E7%9B%AE%E5%BD%95/" title="『算法-ACM竞赛-图论-最短路』最短路算法目录">
                        <span class="hidden-mobile">『算法-ACM竞赛-图论-最短路』最短路算法目录</span>
                        <span class="visible-mobile">下一篇</span>
                        <i class="iconfont icon-arrowright"></i>
                      </a>
                    
                  </article>
                </div>
              
            </div>

            
  
  
    <article id="comments" lazyload>
      
  <div id="valine"></div>
  <script type="text/javascript">
    Fluid.utils.loadComments('#valine', function() {
      Fluid.utils.createScript('https://lib.baomitu.com/valine/1.5.1/Valine.min.js', function() {
        var options = Object.assign(
          {"appId":"fIfc7WqUDZohlQuPc2lz5mJy-MdYXbMMI","appKey":"zjlAG3ZA3o4cBHVAkjzc2Z20","path":"window.location.pathname","placeholder":"留言仅限讨论，禁止广告等行为","avatar":"retro","meta":["nick","mail","link"],"requiredFields":[],"pageSize":10,"lang":"zh-CN","highlight":false,"recordIP":false,"serverURLs":"https://fifc7wqu.api.lncldglobal.com","emojiCDN":null,"emojiMaps":null,"enableQQ":false},
          {
            el: "#valine",
            path: window.location.pathname
          }
        )
        new Valine(options);
        Fluid.utils.waitElementVisible('#valine .vcontent', () => {
          var imgSelector = '#valine .vcontent img:not(.vemoji)';
          Fluid.plugins.imageCaption(imgSelector);
          Fluid.plugins.fancyBox(imgSelector);
        })
      });
    });
  </script>
  <noscript>Please enable JavaScript to view the comments</noscript>


    </article>
  


          </article>
        </div>
      </div>
    </div>

    <div class="side-col d-none d-lg-block col-lg-2">
      
  <aside class="sidebar" style="margin-left: -1rem">
    <div id="toc">
  <p class="toc-header">
    <i class="iconfont icon-list"></i>
    <span>目录</span>
  </p>
  <div class="toc-body" id="toc-body"></div>
</div>



  </aside>


    </div>
  </div>
</div>





  



  



  



  



  







    

    
      <a id="scroll-top-button" aria-label="TOP" href="#" role="button">
        <i class="iconfont icon-arrowup" aria-hidden="true"></i>
      </a>
    

    
      <div class="modal fade" id="modalSearch" tabindex="-1" role="dialog" aria-labelledby="ModalLabel"
     aria-hidden="true">
  <div class="modal-dialog modal-dialog-scrollable modal-lg" role="document">
    <div class="modal-content">
      <div class="modal-header text-center">
        <h4 class="modal-title w-100 font-weight-bold">搜索</h4>
        <button type="button" id="local-search-close" class="close" data-dismiss="modal" aria-label="Close">
          <span aria-hidden="true">&times;</span>
        </button>
      </div>
      <div class="modal-body mx-3">
        <div class="md-form mb-5">
          <input type="text" id="local-search-input" class="form-control validate">
          <label data-error="x" data-success="v" for="local-search-input">关键词</label>
        </div>
        <div class="list-group" id="local-search-result"></div>
      </div>
    </div>
  </div>
</div>

    

    
  </main>

  <footer>
    <div class="footer-inner">
  
    <div class="footer-content">
       <meta name="referrer" content="no-referrer" /> <footer id="footer" role="contentinfo"> <div class="divider"> <div class="wall"></div> <img class="animals" src="/img/footer_animals_new.png" srcset="/img/loading.gif" lazyload alt="Footer Animals"> </div> <div class="container" data-index="450"> <p> <a href="https://chiamzhang.github.io" target="_blank">DogEgg</a> <i class="iconfont icon-love"></i> <a href="#" target="_blank">LittePig</a> </p> <p> Powered by  <a href="https://hexo.io" target="_blank" rel="nofollow noopener"><span>Hexo</span></a> <i class="iconfont icon-pen"></i> Theme  <a href="https://github.com/fluid-dev/hexo-theme-fluid" target="_blank" rel="nofollow noopener"><span>Fluid</span></a> </p> </div> </footer> 
    </div>
  
  
  
  
</div>

  </footer>

  <!-- Scripts -->
  
  <script  src="https://lib.baomitu.com/nprogress/0.2.0/nprogress.min.js" ></script>
  <link  rel="stylesheet" href="https://lib.baomitu.com/nprogress/0.2.0/nprogress.min.css" />

  <script>
    NProgress.configure({"showSpinner":false,"trickleSpeed":100})
    NProgress.start()
    window.addEventListener('load', function() {
      NProgress.done();
    })
  </script>


<script  src="https://lib.baomitu.com/jquery/3.6.4/jquery.min.js" ></script>
<script  src="https://lib.baomitu.com/twitter-bootstrap/4.6.1/js/bootstrap.min.js" ></script>
<script  src="/js/events.js" ></script>
<script  src="/js/plugins.js" ></script>


  <script  src="https://lib.baomitu.com/typed.js/2.0.12/typed.min.js" ></script>
  <script>
    (function (window, document) {
      var typing = Fluid.plugins.typing;
      var subtitle = document.getElementById('subtitle');
      if (!subtitle || !typing) {
        return;
      }
      var text = subtitle.getAttribute('data-typed-text');
      
        typing(text);
      
    })(window, document);
  </script>




  
    <script  src="/js/img-lazyload.js" ></script>
  




  
<script>
  Fluid.utils.createScript('https://lib.baomitu.com/tocbot/4.20.1/tocbot.min.js', function() {
    var toc = jQuery('#toc');
    if (toc.length === 0 || !window.tocbot) { return; }
    var boardCtn = jQuery('#board-ctn');
    var boardTop = boardCtn.offset().top;

    window.tocbot.init(Object.assign({
      tocSelector     : '#toc-body',
      contentSelector : '.markdown-body',
      linkClass       : 'tocbot-link',
      activeLinkClass : 'tocbot-active-link',
      listClass       : 'tocbot-list',
      isCollapsedClass: 'tocbot-is-collapsed',
      collapsibleClass: 'tocbot-is-collapsible',
      scrollSmooth    : true,
      includeTitleTags: true,
      headingsOffset  : -boardTop,
    }, CONFIG.toc));
    if (toc.find('.toc-list-item').length > 0) {
      toc.css('visibility', 'visible');
    }

    Fluid.events.registerRefreshCallback(function() {
      if ('tocbot' in window) {
        tocbot.refresh();
        var toc = jQuery('#toc');
        if (toc.length === 0 || !tocbot) {
          return;
        }
        if (toc.find('.toc-list-item').length > 0) {
          toc.css('visibility', 'visible');
        }
      }
    });
  });
</script>


  <script src=https://lib.baomitu.com/clipboard.js/2.0.11/clipboard.min.js></script>

  <script>Fluid.plugins.codeWidget();</script>


  
<script>
  Fluid.utils.createScript('https://lib.baomitu.com/anchor-js/4.3.1/anchor.min.js', function() {
    window.anchors.options = {
      placement: CONFIG.anchorjs.placement,
      visible  : CONFIG.anchorjs.visible
    };
    if (CONFIG.anchorjs.icon) {
      window.anchors.options.icon = CONFIG.anchorjs.icon;
    }
    var el = (CONFIG.anchorjs.element || 'h1,h2,h3,h4,h5,h6').split(',');
    var res = [];
    for (var item of el) {
      res.push('.markdown-body > ' + item.trim());
    }
    if (CONFIG.anchorjs.placement === 'left') {
      window.anchors.options.class = 'anchorjs-link-left';
    }
    window.anchors.add(res.join(', '));

    Fluid.events.registerRefreshCallback(function() {
      if ('anchors' in window) {
        anchors.removeAll();
        var el = (CONFIG.anchorjs.element || 'h1,h2,h3,h4,h5,h6').split(',');
        var res = [];
        for (var item of el) {
          res.push('.markdown-body > ' + item.trim());
        }
        if (CONFIG.anchorjs.placement === 'left') {
          anchors.options.class = 'anchorjs-link-left';
        }
        anchors.add(res.join(', '));
      }
    });
  });
</script>


  
<script>
  Fluid.utils.createScript('https://lib.baomitu.com/fancybox/3.5.7/jquery.fancybox.min.js', function() {
    Fluid.plugins.fancyBox();
  });
</script>


  <script>Fluid.plugins.imageCaption();</script>

  <script  src="/js/local-search.js" ></script>




  
<script src="/js/love.js"></script>
<script src="/js/funnyTitle.js"></script>
<script src="/js/backTop.js"></script>
<script src="//cdn.jsdelivr.net/gh/bynotes/texiao/source/js/xiaoxuehua.js"></script>



<!-- 主题的启动项，将它保持在最底部 -->
<!-- the boot of the theme, keep it at the bottom -->
<script  src="/js/boot.js" ></script>


  

  <noscript>
    <div class="noscript-warning">博客在允许 JavaScript 运行的环境下浏览效果更佳</div>
  </noscript>
<script src="/live2dw/lib/L2Dwidget.min.js?094cbace49a39548bed64abff5988b05"></script><script>L2Dwidget.init({"pluginRootPath":"live2dw/","pluginJsPath":"lib/","pluginModelPath":"assets/","tagMode":false,"debug":false,"model":{"jsonPath":"/live2dw/assets/wanko.model.json"},"display":{"position":"left","width":150,"height":150,"hOffset":20,"vOffset":0},"mobile":{"show":false,"scale":0.5},"react":{"opacity":0.9},"log":false});</script></body>
</html>
